Grier got his start on the National Public Radio radio drama adaptation of Star Wars in 1980. He was the voice of a nameless X-wing fighter pilot during the Battle of Yavin.
Grier's later first taste of star life was in a short-lived Broadway musical called The First where he played famed black baseball player Jackie Robinson. He received a Tony nomination for his performance. He later starred as James "Thunder" Early in the hit Broadway musical Dreamgirls (a role which would later be played in the movie version by Eddie Murphy).
Then after a series of movie & TV appearances, he got a job that really got him noticed. It was the job of one of the cast members of the FOX variety show, In Living Color.
While doing the show, more movie & TV roles followed including the role of shoe factory worker turned police officer and back again Carl Bentley in the 1995 film Jumanji.